Frequency-Enhanced Hilbert Scanning Mamba for Short-Term Arctic Sea Ice Concentration Prediction

TL;DR

This work introduces FH-Mamba, a Frequency-enhanced Hilbert Scanning Mamba framework for short-term Arctic SIC forecasting that explicitly models temporal locality via a 3D Hilbert scanning mechanism, enhances edge details with a wavelet-based frequency branch, and fuses sequence and frequency information through Hybrid Shuffle Attention. The approach achieves state-of-the-art performance on OSI-450a1 and AMSR2 datasets, with strong improvements in RMSE, MAE, and NSE, and demonstrates sharper boundary preservation in marginal ice zones. Comprehensive ablations, efficiency analyses, and an uncertainty-quantification extension validate the robustness and practicality of the method, with code released for public use. Overall, FH-Mamba offers a scalable, accurate, and edge-aware solution for spatiotemporal Arctic SIC prediction with potential broader applicability to climate-data forecasting.

Abstract

While Mamba models offer efficient sequence modeling, vanilla versions struggle with temporal correlations and boundary details in Arctic sea ice concentration (SIC) prediction. To address these limitations, we propose Frequency-enhanced Hilbert scanning Mamba Framework (FH-Mamba) for short-term Arctic SIC prediction. Specifically, we introduce a 3D Hilbert scan mechanism that traverses the 3D spatiotemporal grid along a locality-preserving path, ensuring that adjacent indices in the flattened sequence correspond to neighboring voxels in both spatial and temporal dimensions. Additionally, we incorporate wavelet transform to amplify high-frequency details and we also design a Hybrid Shuffle Attention module to adaptively aggregate sequence and frequency features. Experiments conducted on the OSI-450a1 and AMSR2 datasets demonstrate that our FH-Mamba achieves superior prediction performance compared with state-of-the-art baselines. The results confirm the effectiveness of Hilbert scanning and frequency-aware attention in improving both temporal consistency and edge reconstruction for Arctic SIC forecasting. Our codes are publicly available at https://github.com/oucailab/FH-Mamba.

Figures (8)

• Figure 1: Comparison of vanilla Mamba and 3D Hilbert scanning. (a) Scanning route by vanilla Mamba. (b) Scanning route by 3D Hilbert. (c) Visualization of SIC prediction. The lines and endpoints are shaded in gradients from red to green, representing the route of the scan. Vanilla Mamba struggles to effectively model temporal correlation of SIC sequences, while our FH-Mamba leverages the 3D Hilbert curve's locality characteristic to enhance the spatiotemporal learning.
• Figure 2: Framework of our Frequency-Enhanced Hilbert scanning Mamba (FH-Mamba) for short-term Arctic sea ice concentration prediction. It is composed of a feature encoder, a series of Frequency-enhanced State Space Module (FSSM), and a feature decoder. The FSSM employs the 3D Hilbert State Space (3DHSS) block and wavelet transform to capture spatio-temporal feature dependencies. In 3DHSS, we use 3D Hilbert scanning mechanism to capture temporal-level local information. Furthermore, Hybrid Shuffle Attention (HSA) module is designed to fuse sequence and frequency features, effectively exploiting their complementary information.
• Figure 3: Trajectories of standard Mamba and 3D Hilbert scanning.
• Figure 4: Illustration of the Hybrid Shuffle Attention (HSA). The input sequence and frequency features $\{\mathbf{x}^1, \mathbf{x}^2, \mathbf{x}^f\}$ are handled by pooling and concatenation to generate $\hat{\mathbf{X}}$. It undergoes the shuffle operation and results in $\hat{\mathbf{X}}'$. Afterwards, $\hat{\mathbf{X}}'$ are split into $D$ groups. Group convolution and unshuffle operation are employed, generating unshuffled weights $\hat{\mathbf{A}}$. The weights are further chunked and reshaped into attention weights $\{\mathbf{A}^1, \mathbf{A}^2, \mathbf{A}^f\}$. Finally, the output is computed by performing weighted summation of the input features and the attention weights.
• Figure 5: The visualization results of VMRNN, FCNet, and our FH-Mamba during the period from September 1 to 14, 2020. The left columns show the predicted SIC maps for each model alongside the ground truth. The right columns highlight the bias maps (prediction minus ground truth). In the bias maps, positive errors are shown in red and negative errors in blue.